Question

the picture below has 3 normal curves plotted on the same set of axes. compare the means of the 3 distributions. compare the standard deviations of the 3 distributions. the three distributions have different values for the mean because each curve has a different center and the three distributions have different standard deviations. the three distributions have different values for the mean because each curve has a different center and the three distributions have the same standard deviation. the three distributions all have the same mean because each curve has the same center and the three distributions have different standard deviations. the three distributions all have the same mean because each curve has the same center and the three distributions have the same standard deviation.

Explanation:

Step1: Recall properties of normal - curve

The mean of a normal distribution is the x - value at the center of the curve. The standard deviation affects the spread of the normal curve. A smaller standard deviation makes the curve taller and narrower, while a larger standard deviation makes the curve shorter and wider.

Step2: Analyze the centers of the curves

Looking at the graph, all three normal curves are centered at the same x - value (around 60). So, the means of the three distributions are the same.

Step3: Analyze the spreads of the curves

The three curves have different spreads. One curve is taller and narrower, another is shorter and wider, and the third has a spread in - between. So, the standard deviations of the three distributions are different.

Answer:

The three distributions all have the same mean because each curve has the same center and the three distributions have different standard deviations.